It's a tough one - and something we need to heed a lesson from - a lot of our stuff is in our heads and if our loved ones are to benefit from our round then we need to keep them in the loop.
Sounds like she is scared stiff of you (understandably) and that you are very suspicious of her (understandably).
Take her out for a coffee (if she is a looker "do lunch darling!"
) and reflect back to her what you think her worries are - say:
Look, I am really interested but if I were you I would be worried sick that someone was out to rip me off. How about we find someone we mutually trust (her accountant - if he's a real accountant and not some geezer she knows), say that you will both share paying him for an half an hour of his time where he is permitted to tell (on a non-disclosure basis) some detail of the business.
If that meeting works out then you both do the same with a solicitor (tell him you're looking for a package deal with an estimate of costs rather than an hourly rate) to iron out the details and draw up a payment agreement/handover agreement.
For a 60K deal it's worth costing each of you a few hundred quid in professional fees.
....
Now - if the round is genuinely paying two full time staff and the daughter is drawing money too then by inference it has to be turning over 6K a month - so is it VAT registered?
If it isn't then are the staff part time? Is she making no money out of it? Is it really worth 60K?
Good Luck!